Laminar and turbulent flow. Flow Modes

The study of the properties of flows of liquids and gases is very important for industry and communal services. Laminar and turbulent flow affects the speed of transportation of water, oil, natural gas through pipelines of various purposes, affects other parameters. The science of hydrodynamics deals with these problems.

Classification

In a scientific environment, the flow regimes of a liquid and gases are divided into two completely different classes:

• Laminar (jet);
• Turbulent.

Also distinguish transitional stage. By the way, the term "liquid" has a wide meaning: it can be incompressible (it's actually a liquid), compressible (gas), conductive, etc.

Background

In 1880 Mendeleyev also expressed the idea of the existence of two opposite flow regimes. The British physicist and engineer Osborne Reynolds studied this matter in more detail, completing the research in 1883. First, practically, and then with the help of formulas he established that, at a low flow velocity, the movement of liquids takes on a laminar form: the layers (particle flows) are hardly mixed and move along parallel trajectories. However, after overcoming a certain critical value (for different conditions it is different), called the Reynolds number, the fluid flow regimes change: the jet stream becomes chaotic, vortex - that is, turbulent. As it turned out, these parameters are to a certain extent peculiar to gases.

Practical calculations of the English scientist have shown that the behavior, for example, of water, strongly depends on the shape and size of the reservoir (pipe, channel, capillary, etc.) through which it flows. In pipes having a circular cross-section (such used for mounting pressure pipelines), its Reynolds number - the critical state formula is described as follows: Re = 2300. For the flow along the open channel, the Reynolds number is different: Re = 900. At lower Re values, the flow will be ordered, At large - chaotic.

Laminar flow

The difference between laminar flow and turbulent flow is in the nature and direction of the water (gas) flows. They move in layers, not mixing and without pulsations. In other words, the motion passes uniformly, without random pressure jumps, direction and speed.

Laminar flow of fluid is formed, for example, in narrow blood vessels of living creatures, plant capillaries and under comparable conditions, during the flow of very viscous liquids (fuel oil through a pipeline). To visually see the jet stream, it is enough to slightly open the water tap - water will flow calmly, evenly, without mixing. If the tap is turned to the end, the pressure in the system will increase and the current will become chaotic.

Turbulent flow

In contrast to laminar flow, in which nearby particles move along practically parallel trajectories, the turbulent flow of a fluid is disordered. If we use the Lagrange approach, the particle trajectories can arbitrarily intersect and behave quite unpredictably. The motions of liquids and gases under these conditions are always nonstationary, and the parameters of these nonstationary states can have a very wide range.

As the laminar flow regime of the gas turns into a turbulent one, one can trace it by the example of a trickle of smoke of a burning cigarette in still air. At first, the particles move practically parallel in time-invariant trajectories. The smoke seems to be motionless. Then in a place suddenly there are large eddies, which move completely chaotically. These vortices break up into smaller ones, those into even smaller ones and so on. In the end, the smoke is practically mixed with the surrounding air.

Cycles of turbulence

The above example is a textbook one, and from his observation the scientists made the following conclusions:

1. The laminar and turbulent flow has a probabilistic nature: the transition from one mode to another does not occur in a precisely defined place, but in a fairly arbitrary, random place.
2. First, large vortices appear, whose size is larger than the size of the trickle of smoke. The motion becomes nonstationary and strongly anisotropic. Large flows lose stability and break down into smaller and smaller ones. Thus, a whole hierarchy of vortices arises. The energy of their motion is transferred from large to small, and at the end of this process disappears - energy dissipation occurs at small scales.
3. The turbulent flow regime is random: one or another vortex can appear in a completely arbitrary, unpredictable place.
4. The mixing of smoke with ambient air practically does not occur under the laminar regime, and when turbulent, it is very intense.
5. Despite the fact that the boundary conditions are stationary, the turbulence itself has a pronounced nonstationary character - all the gasdynamic parameters vary with time.

There is another important property of turbulence: it is always three-dimensional. Even if we consider a one-dimensional flow in a pipe or a two-dimensional boundary layer, the motion of turbulent eddies still flows in the directions of all three coordinate axes.

Reynolds number: formula

The transition from laminarity to turbulence is characterized by the so-called critical Reynolds number:

Re _cr = (ρuL / μ) _cr,

Where ρ is the flux density, u is the characteristic flow velocity; L is the characteristic flow size, μ is the coefficient of dynamic viscosity, and cr is the flow along a pipe with a circular cross section.

For example, for a flow with velocity u in a pipe, the pipe diameter is used as L. Osborne Reynolds showed that in this case 2300 cr <20000. The spread is very large, almost an order of magnitude.

A similar result is obtained in the boundary layer on the plate. The characteristic dimension is the distance from the leading edge of the plate, and then: 3 × 10 ⁵ cr <4 × 10 ⁴ . If L is defined as the thickness of the boundary layer, then 2700 cr <9000. There are experimental studies that showed that the value of Re _cr may be even greater.

The notion of velocity perturbation

The laminar and turbulent flow of the liquid, and therefore the critical value of the Reynolds number (Re), depends on a greater number of factors: the pressure gradient, the height of the roughness knots, the turbulence in the external flow, the temperature difference, etc. For convenience, these total factors are also called velocity perturbations , Since they have a certain effect on the flow velocity. If this perturbation is small, it can be extinguished by viscous forces tending to equalize the velocity field. For large perturbations, the flow can lose stability, and turbulence arises.

Bearing in mind that the physical meaning of the Reynolds number is the ratio of inertial forces and viscosity forces, the perturbation of the flows is subject to the formula:

Re = ρuL / μ = ρu ² / (μs (u / L)).

In the numerator there is a doubled velocity head, and in the denominator there is a quantity of the order of the frictional stress, if the thickness of the boundary layer is taken as L. High-speed pressure tends to destroy the balance, and friction forces counteract this. However, it is not clear why the forces of inertia (or high-speed head) lead to changes only when they are 1000 times greater than the viscosity forces.

Calculations and facts

Probably, it would be more convenient to use as the characteristic velocity in Re _cr not the absolute flow velocity u, but the velocity perturbation. In this case, the critical Reynolds number will be of the order of 10, that is, if the velocity head exceeds the viscous stresses by a factor of 5, the laminar flow of the liquid flows into a turbulent one. This definition of Re in the opinion of a number of scientists explains well the following experimentally confirmed facts.

For an ideally uniform velocity profile on an ideally smooth surface, the traditionally determined number Re _cr tends to infinity, that is, there is virtually no transition to turbulence. But the Reynolds number, determined by the magnitude of the velocity perturbation is less than the critical one, which is equal to 10.

In the presence of artificial turbulators, which cause a speedup comparable to the main velocity, the flow becomes turbulent at much lower values of the Reynolds number than Re _cr , determined from the absolute value of the velocity. This allows us to use the value of the coefficient Re _cr = 10, where the absolute speed perturbation value, caused by the above mentioned reasons, is used as the characteristic velocity.

Stability of laminar flow in the pipeline

Laminar and turbulent flow is typical for all types of liquids and gases in different conditions. In nature, laminar flows are rare and typical, for example, for narrow underground flows in flat conditions. Much more this issue is of concern to scientists in the context of practical applications for transporting water, oil, gas and other technical fluids through pipelines.

The stability of laminar flow is closely connected with the investigation of the perturbed motion of the main flow. It is established that it is subjected to so-called small perturbations. Depending on whether they fade or grow with time, the main current is considered stable or unstable.

Flow of compressible and non-compressible liquids

One of the factors affecting the laminar and turbulent flow of a fluid is its compressibility. This property of a liquid is especially important in the study of the stability of nonstationary processes with a rapid change in the fundamental flow.

Studies show that the laminar flow of an incompressible fluid in cylindrical tubes is stable to relatively small axisymmetric and non-axisymmetric perturbations in time and space.

Recently, calculations have been carried out on the effect of axisymmetric perturbations on the stability of flow in the inlet part of a cylindrical tube, where the main flow is dependent on two coordinates. The coordinate along the pipe axis is considered as a parameter on which the velocity profile depends on the radius of the main flow pipe.

Conclusion

Despite the centuries of study, it can not be said that both laminar and turbulent flows have been thoroughly studied. Experimental research at the micro level poses new questions that require a reasoned rationale. The nature of the research is also of practical use: thousands of kilometers of water, oil, gas, and product pipelines are laid in the world. The more technical solutions to reduce turbulence during transportation, the more effective it will be.